Question 1

An agency is having problems with personal phone calls made during working hours. Each minute of a personal call costs the agency $0.50 in wasted wages. The agency decides to hire operators to monitor calls in order to attain the optimal number of personal calls (minimize total cost of personal calls).

Number of Operators / Total minutes of personal calls
(per hour)
0 / 700
1 / 570
2 / 460
3 / 370
4 / 300
5 / 250

A- What is the most the agency would be willing to pay the first operator?

B- If operators receive $38 an hour, how many operators should the agency hire?

C--Assume a change in the operator labor market results in operator wages rising to $47 an hour; what is the optimal number of operators the agency should hire after the wage change?

Consider whether the wage change is a change in marginal benefit or marginal cost.

D- Assume that operators receive $38 an hour again, but that the cost of personal calls rises to $0.75 in wasted wages. How many operators should the agency hire now?

Question 2

Bavarian Crystal Works designs and produces lead crystal wine decanters for export to international markets. The production manager of Bavarian Crystal Works estimates total and marginal production costs to be

TC = 10,000 + 40Q + 0.0025Q2

and

MC = 40 + 0.005Q

where costs are measured in U.S. dollars and Q is the number of wine decanters produced annually. Because Bavarian Crystal Works is only one of many crystal producers in the world market, it can sell as many of the decanters as it wishes for $70 apiece. Total and marginal revenue are

TR = 70Q

and

MR = 70

where revenues are measured in U.S. dollars and Q is annual decanter production.

A -What is the optimal level of production of wine decanters?

B - What is the marginal revenue from the last wine decanter sold?

C-What is the total revenue from selling the optimal number of wine decanters?

D- What is the total cost from selling the optimal number of wine decanters?

C- What is the net benefit (profit) from selling the optimal number of wine decanters?

Question 3

At the optimal level of production of decanters, an extra decanter can be sold for $70, thereby increasing total revenue by $70.Why would the manager of this firm not produce and sell either one more or one less unit?

Select one:

a. Profit increases, but costs increase more rapidly.

b. Net benefit becomes negative.

c. At any levelotherthan the optimum, total cost exceeds total revenue.

d. It reduces net benefit (profit).

Question 4

The director of marketing at Vanguard Corporation believes that sales of the company’s Bright Side laundry detergent (S) are related to Vanguard’s own advertising expenditures (A), as well as the combined advertising expenditures of its three biggest rival detergents (R). The marketing director collects 36 weekly observations on S, A, and R to estimate the following multiple regression equation:

S = a + bA + cR

where S, A, and R are measured in dollars per week. Vanguard’s marketing director is comfortable using parameter estimates that are statistically significant at the 10 percent level or better.

A-The expected sign of

Select one:

a. ais positive,bis negative, andcis positive.

b. ais positive,bis positive, andcis positive.

c. a is positive, b is positive, and c is negative.

d. ais negative,bis positive, andcis negative.

Question 5

The regression output from the computer is as follows:

Dep. Var.: S / R-square / F-ratio / p-value on F
observations: 36 / 0.2247 / 4.781 / 0.0150
Variable / Parameter Estimate / Standard Error / T-ratio / P-value
Intercept / 175086.0 / 63821.0 / 2.74 / 0.0098
A / 0.8550 / 0.3250 / 2.63 / 0.0128
B / -0.284 / 0.164 / -1.73 / 0.0927

A -The estimated coefficient for a (intercept) suggests that

Select one:

a. If A and R are zero, Vanguard could still expect about $175,086 in sales per week.

b. Sales will be$175,086 per week when A and R are at their maximum values.

c. a cannot be interpreted with confidence since its parameter estimate is not statistically significant.

d. Sales will range between $63,821 and $175,086 per week, but not outside those limits.

B-The estimated coefficient for b (own advertising expenditures A) suggests that

Select one:

a. An increase of $855 of own advertising expenditures will reduce rival advertising expenditures by $284.

b. own advertising expenditures is inelastic since its parameter estimate is less than 1.

c. a $1,000 increase in own advertising expenditures is associated with an increase of weekly sales of $855.

d. if own advertising expenditures is increased by $855, sales will increase by $1,000.

C-The estimated coefficient for c (rival advertising expenditures R) suggests that

Select one:

a. a $284 decrease incombined rival advertising expenditures is associated with a $1,000 increase in Vanguard’s weekly sales.

b. a $1,000 increase in combined rival advertising expenditures is associated with a $284 drop in Vanguard’s weekly sales.

c. combined rival advertising expenditures follows the law of demand since its parameter estimate is negative as expected.

d. when Vanguard increases its advertising expenditures by $1,000, its rivals reduce theirs by $284.

D-Vanguard’s advertising expenditure has a statistically significant effect on the sales of Bright Side detergent.

Select one:

True

False

E-Combined advertising expenditures by its three largest rivals affects sales of Bright Side detergent in a statistically significant way.

Select one:

True

False

F-What fraction of the total variation in sales of Bright Side remains unexplained?

Select one:

a. 4.781%

b. 0.2247, or 22.47%

c. 0.7753, or 77.53%

d. 1/0.2247 = 4.45%

G- What is the expected level of sales each week when Vanguard spends $40,000 per week and the combined advertising expenditures for the three rivals are $100,000 per week?

Question 6

Download the “Soft Drink Consumption” Excel sheet. Estimate the following multiple regression models (remember that all of your independent variables will have to be in adjacent columns in Excel). Look at each set of results critically and consider how you would interpret the strengths and weaknesses of each model. Save your results from each model for use when completing the end-of-module assessment. C, the dependent variable, will always be “Consumption of Soft Drinks per Capita;” for independent variables, use the following specifications. (The notation f(X, Y, Z) means “a function of X, Y, Z; i.e., X, Y, and Zare your independent variables. Even though it isn’t listed, each model will include an intercept.)NOTE: when Excel reports a value like 2.4E-06, this is scientific notation for 2.4 * (10^-6), or 0.0000024.

Model A: C = f(% obese, dentists, physicians)

Model B: C = f(food services, % smokers total)

Model C: C = f(food services, % male smokers, % female smokers)

Model D: C = f(food services, % smokers total, % male smokers)

Model E: C = f(per capita income, mean annual temp)

Model F: C = f(mean annual temp, % obese, dentists, food services, % male smokers)

Model G: C = f(mean annual temp, % obese, dentists, food services, % smokers total)

A- In model A, how much of the variation in soft drink consumption is explained by% obese, dentists, and physicians?

Select one:

a. 0.0226%

b. 24.4%

c. 10.2%

d. 30.9%

B- How would you interpret the coefficient for dentists?

Select one:

a. As the number of dentists increases by 1 per 1000 people, annual soft drink consumption increases by about 2.85% per year.

b. As the number of dentists increases by 1 per 1000 people, annual soft drink consumption decreases by about 2.265% per year.

c. When the number of dentists per 1000 people decreases by about 175, then soft drink consumption per capita is expected to increase by 1 unit annually.

d. As the number of dentists increases by 1 per 1000 people, annual soft drink consumption decreases by about 175 per year.

C- The coefficient for physicians per 100,000 is statistically significant at the 10% level.

Select one:

True

False

D- What seems to be the relationship between soft drink consumption and the percent who smoke?

Select one:

a. It is difficult to draw any conclusions because the smoker variables were all insignificant (at the 10% level) in all models.

b. As the % smokers rise, soft drink consumption increases, since all of the smoking coefficients in models B-D were positive.

c. For the smoker variables that are statistically significant, the relationship between % smokers and soft drink consumption appears to be negative.

d. % smokers in total seems important (in model B), but once you separate male vs. female smokers it appears that it is only % male smokers that is significantly related to soft drink consumption.

E- A state that currently has 11,000 food service businesses also currently has 20% of its population who smoke (total, both male and female). The state is considering a major initiative to reduce its smoking population to 15%. If it is successful, this will also cause soft drink consumption to fall from about 165 drinks annually to about Answer drinks annually (round to nearest whole number, no decimals).

F-The relationship between number of food service businesses and soft drink consumption per capita

Select one:

a. is negative since, because all of the estimated coefficients were positive, the fact that they were insignificant (at the 10% level) means that you switch the signs.

b. is unimportant since, even though it was statistically significant, its coefficient estimate was always small.

c. is negatively or inversely related since the intercept was always negative in models B-D.

d. is difficult to summarize because it was insignificant (at the 10% level) in models B-D.

Question text

Of all the variables in models E through G, mean annual temperature is the only one that is statistically significant (at the 10% level).

Select one:

True

False

G- In models B-D, it was seen that male smokers was significant. With additional variables added in models E-G, % male smokers

Select one:

a. still has a positive coefficient but is insignificant (at the 10% level).

b. has about the same effect on soft drink consumption as does mean annual temperature.

c. is significant but negatively related to soft drink consumption.

d. is insignificant (at the 10% level) while total smokers is now significant.

H- While highly significant in model A, % obese is insignificant (at the 10% level) in models F and G.

Select one:

True

False

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